Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Consistent Model-based Clustering using the Quasi-Bernoulli Stick-breaking Process
Authors: Cheng Zeng, Jeffrey W Miller, Leo L Duan
JMLR 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In simulations and a data application of clustering brain networks, our proposed method recovers the ground-truth number of clusters, and leads to a small number of clusters. Keywords: Consistent Clustering, Exchangeable Partition Probability Function, Sparse Simplex. |
| Researcher Affiliation | Academia | Cheng Zeng EMAIL Department of Statistics University of Florida Gainesville, FL 32611, USA Jeffrey W Miller EMAIL Department of Biostatistics Harvard T.H. Chan School of Public Health Boston, MA 02115, USA Leo L Duan EMAIL Department of Statistics University of Florida Gainesville, FL 32611, USA |
| Pseudocode | Yes | 3. Posterior Sampling Algorithm Since the quasi-Bernoulli mixture model involves a small modification to classic stickbreaking construction, we can use an efficient slice sampling algorithm [Kalli et al. (2011), as the improved version of Walker (2007)] for posterior inference. We use a sequence of decreasing positive constants ξ1, ξ2, . . . that converges to zero. In this article, we choose ξi = 0.5i for i ≥ 1 as suggested in Kalli et al. (2011). Given ci (the component assignment), consider a latent uniform ui Uniform(0, ξci), then we have a joint likelihood proportional to Πn i=1 1(ui < ξci)wci/ξcifθci(yi). We define the state of the Markov chain to be (c, θ, w, u) and the target distribution is the posterior p(c, θ, w, u | y), where y = y1:n, c = c1:n, θ = θ1:∞, and w = w1:∞. The slice sampler iterates the following steps: 1. Sample c from its full conditional. For i = 1, . . . , n: sample ci Categorical( wk) where wk = wk/ξkfθk(yi) / P {l:ξl>ui} wl/ξlfθl(yi), for k ∈ {l : ξl > ui}. Since the sequence ξ1, ξ2, . . . converges to zero, the index set {l : ξl > ui} is finite. Compute nk := P i 1(ci = k), and mk := P i 1(ci > k). 2. Sample u from its full conditional. For i = 1, . . . , n: sample ui from the uniform distribution over the interval (0, ξci). 3. Sample w from its full conditional. For k ∈ n i=1{l : ξl > ui}: Sample bk ∼ qδ1( ) + (1 − q)δϵ( ) where q = p / (p + (1 − p)ϵαIϵ(mk + α, nk + 1)). Sample βk by drawing X ∼ Beta(0,bk)(mk + α, nk + 1) and setting βk = X/bk, where Beta(0,ϵ) denotes a Beta distribution truncated to the interval (0, ϵ). Compute wk from b1:k and β1:k using Equation (2). 4. Sample θ from its full conditional. For k ∈ n i=1{l : ξl > ui}: sample θk from the distribution proportional to g(θk) Π i:ci=k fθk(yi), where g is the density of the base measure G. |
| Open Source Code | Yes | A software implementation and the steps needed to replicate the results in this paper are provided on https://github.com/zengcheng/quasi-bernoulli-stick-breaking. |
| Open Datasets | Yes | To demonstrate the ease of using our model in an advanced data analysis, we apply it to cluster multiple brain networks, collected from n = 812 subjects in the human connectome project (Marcus et al., 2011). |
| Dataset Splits | No | We first generate data with sample sizes n ∈ {50, 100, 250, 1000, 2500} from a threecomponent univariate Gaussian mixture distribution: 0.3 N(−4, 1^2)+0.3 N(0, 1^2)+0.4 N(5, 1^2). (Section 4.1) To demonstrate the ease of using our model in an advanced data analysis, we apply it to cluster multiple brain networks, collected from n = 812 subjects in the human connectome project (Marcus et al., 2011). (Section 5) |
| Hardware Specification | Yes | The algorithms are implemented in R, and run on a 4.0 GHz processor. |
| Software Dependencies | No | The algorithms are implemented in R, and run on a 4.0 GHz processor. |
| Experiment Setup | Yes | We set p = 0.9 for the quasi-Bernoulli probability in Equation (2), yielding a prior mean of no more than 1/(1 − p) = 10 components with mixture weights larger than ϵ. ... We set α = 1 and ϵ = 1/n^2.1, which satisfies the theoretical condition that ϵ = o(1/n^2) in Theorem 5. ... For each experiment, we run the Markov chain for 50,000 iterations, discard the first 20,000 as burn-ins, and use thinning by keeping only every 50th iteration. (Section 4) For the quasi-Bernoulli prior on w, we use p = 0.9, α = 1 and ϵ = 1/n^2.1. We run the MCMC sampler from Section 3 for 30, 000 iterations and discard the first 10, 000 as burn-ins. (Section 5) |